Download Ampere`s Law, etc. Ampère`s Law - McMaster Physics and Astronomy

Ampere’s Law, etc.
Text 30.3 - 30.5
• Ampere’s Law examples
• Magnetic Flux and Gauss’s Law for magnetism
Practice:
Chapter 30, problems 35, 37, 39, 47, 57.
Ampère’s Law
1
Review quiz:
The integral in Ampere’s Law must be taken
A)  over any closed surface
B)  along a current-carrying wire in any closed circuit
C)  along any current-carrying wire
D)  along any closed curve
Calculating B from Ampere’s Law
For a few simple shapes, we can calculate the field B
easily from Ampere’s Law. The steps:
i)  use symmetry to deduce the general behaviour
ii)  pick a closed curve on which to apply Ampere’s Law,
taking advantage of the symmetry
iii)  Calculate
(in terms of |B|)
iv)  Calculate Iencircled
v)  Apply Ampere’s Law to get B
2
Quick Quizzes
What is the magnetic field inside and outside
1)  a hollow copper pipe carrying current I?
2)  a coaxial cable carrying equal currents (in opposite
directions) on the inner and outer conductors?
Single Coil:
B
I
Several Coils:
x
x
x
x
x
3
d
l
a I out of page
b
c
B
xxxxxxxxxxxxxxxx
I into page
Outside: B≈ 0
Inside: B is uniform, parallel to solenoid axis
d
c
l
aI
b
B
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On which sides of the green rectangle is
not zero?
A)  bc and ad
B)  bc
C)  ad
D)  ab, bc, and cd
E)  none of the above is completely correct
4
l
d
a
I
b
c
B
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The “current encircled” by the green rectangle shown is
A) equal to I
B) equal to 6I
C) equal to zero
d
c
l
a I out of page
b
B
xxxxxxxxxxxxxxxx
I into page
Outside: B≈ 0
Inside: B = µ0nI (uniform, parallel to solenoid axis)
where n = number of turns per metre of length
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Example:
I = 1 amp, n = 100 turns/cm (1x104 turns/m)
Quiz: What is the field at the end of the solenoid, on
the axis ?
A)  130 gauss
B)  65 gauss
C)  260 gauss
D)  zero
B
r
B
path of
integration for
Show that, inside the toroid,
(N = total number of
turns)
6
Flux through a surface S:
( dA is the “area vector”, perpendicular to the surface.)
-  a scalar ; units, 1 T·m2 = 1 weber (Wb)
-  represents “number of field lines through S”
The magnetic flux through
any closed surface is zero.
This is equivalent to:
- the field lines form closed loops
- there are no isolated magnetic poles
(“magnetic monopoles”)
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A beam of fast protons is also a current. Electric
forces cause the beam to widen. The magnetic
forces tend to
A)  cause the beam to spread even more
B)  cause the beam to spread less
C)  have no effect on the spreading
What about a beam of fast electrons?
At what speed v is the total force zero?
FE
v
+
FM
R
+
v
“current element” Ι Δs = qv
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